document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964315>Question 964315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know where else to turn, I've asked my tutors my teacher and peers to explain how to graph sin,cos,sec,csc,tan,cot with phase shifts but nothing seems to work or I am just stupid...how do I set them up? my main confusing is all to do with the phase shifts, everything else makes sense to me. I know the amp, the periodicity. But it's when it comes to  shifting everything right or left where the confusion sets in. The process of doing this is troublesome and I keep hitting brick walls. For instance, my teacher asked us to draw the graph of: y=10tan(3t-pi/8) I know I would rerrange like y=10tan3(t-pi/24) but after that I wouldn't know what to do, I just want to know what the points are going to be on the graph and how to derive them...I am at my witts end here. Please help me understand.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589252 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The best place to start is to first graph the basic function without any shifting.<BR>\n" );
document.write( "For example, take the tan function your teacher gave you: y=10tan(3t-pi/8)<BR>\n" );
document.write( "This equation takes the form: y=A*tan(Bx-C), A=multiplier, period=&#960;/B, C/B=phase shift<BR>\n" );
document.write( "For your given tan function: period=&#960;/B=&#960;/3<BR>\n" );
document.write( "1/4 period=(&#960;/3)/4=&#960;/12&#8776;0.26<BR>\n" );
document.write( "coordinates for one period: (-&#960;/6, u.d.), (-&#960;/12, -1), (0, 0), (&#960;/12, 1), (&#960;/6, u.d.)<BR>\n" );
document.write( "multiply y-coordinates by 10: (-&#960;/6, u.d.), (-&#960;/12, -10), (0, 0), (&#960;/12, 10), (&#960;/6, u.d.)<BR>\n" );
document.write( "phase shift=C/B=(&#960;/8)/3=&#960;/24 (shift to right)<BR>\n" );
document.write( "coordinates for final configuration: (-3&#960;/24, u.d.), (-&#960;/24, -10), (&#960;/24, 0), (3&#960;/24, 10), (5&#960;/24, u.d.)<BR>\n" );
document.write( "u.d.=undefined<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Form of equation for sin: y= Asin(Bx-C), A=amplitude, Period=2&#960;/B, Phase shift=C/B<BR>\n" );
document.write( "Form of equation for cos: y= Acos(Bx-C), A=amplitude, Period=2&#960;/B, Phase shift=C/B<BR>\n" );
document.write( "note: this is just one of the ways I do it. There may be other ways. Hope this helps. </SPAN>\n" );
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